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LegendreQ

  • LegendreQ[ n , z ] gives the Legendre function of the second kind .
  • LegendreQ[ n , m , z ] gives the associated Legendre function of the second kind .
  • Mathematical function (see Section A.3.10).
  • For integer n and m, explicit formulas are generated.
  • The Legendre functions satisfy the differential equation .
  • LegendreQ[ n , m , a , z ] gives Legendre functions of type a. The default is type 1.
  • LegendreQ of types 1, 2 and 3 are defined in terms of LegendreP of these types, and have the same branch cut structure.
  • See the Mathematica book: Section 3.2.10.

    Further Examples

    This gives the second associated Legendre function of the second kind in the variable z.

    In[1]:=

    Out[1]=

    This gives the first associated Legendre function of the second kind.

    In[2]:=

    Out[2]=

    This is the derivative.

    In[3]:=

    Out[3]=

    This is a series expansion around .

    In[4]:=

    Out[4]=